Conventionally a method called as "controlled rolling" has been applied for production of a high strength and toughness (tenacity) steel, according to which method the steel slab is heated to about 1250.degree. C and the finishing rolling temperature is restricted.
However, this conventional method is inherently a temperature controlling method so that subsequent working steps can not be performed until the temperature of the steel material lowers to a certain temperature, thus suffering from remarkably low productivity, and the steel products thus obtained have considerable variation in their quality.
The present inventors have conducted various extensive experiments and studies for the purpose of developing a steel having excellent strength and toughness with less variation, and have found that when a steel slab obtained by continuous casting of a molten steel containing Al and N is heated to a temperature not higher than 1150.degree. C and rolled, the nuclearation of AlN takes precedence over the growth of AlN and fine AlN is formed, thus giving a rolled steel material having excellent strength and toughness.